1. Field of the Invention
This disclosure relates to filter synthesizers for frequency response systems, and in particular, to an apparatus and method for estimating modal parameters of a transfer function to generate stable filters.
2. Description of the Related Art
Frequency response systems, i.e. mechanical, acoustical, or electrical system having an output value dependent on an input frequency, may be modelled as filters on the frequency response data by transfer functions of the input frequencies. Transfer functions or frequency response functions may be formulated in terms of modal parameters such as number of modes, undamped natural frequency, damping ratio, and residues, or zeroes and poles, and equivalently may be formulated as the ratio of polynomials, with such formulations of the transfer function allowing a corresponding filter to be constructed or synthesized which indicates the general behavior of the frequency response system.
However, for systems requiring higher order polynomials and/or equations to accurately model the input frequency response data, calculation of the transfer function or filter from the corresponding frequency response data may be computational ill-conditioned due to numerical round-off errors.
The computed filter may also have unstable poles, making the filter unstable. The disclosed system and method creates stable filters.